In ‎the present ‎paper, ‎we ‎introduce the ‎two-wavelet ‎localization ‎operator ‎for ‎the square ‎integrable ‎representation ‎of a‎ ‎homogeneous space‎ with respect to a relatively invariant measure. ‎We show that it is a bounded linear operator. We investigate ‎some ‎properties ‎of the ‎two-wavelet ‎localization ‎operator ‎and ‎show ‎that ‎it ‎is a‎ ‎compact ‎operator ‎and is ‎contained ‎in‎ a...

In this paper, we consider the optimal disturbance rejection problem for (possibly infinite dimensional) linear time-varying (LTV) systems using a framework based on operator algebras of classes of bounded linear operators. After reducing the problem to a shortest distance minimization in a space of bounded linear operators, duality theory is applied to show existence of optimal solutions, whic...

For each S ∈ L(E) (with E a Banach space) the operator R(S) ∈ L(E/E) is defined by R(S)(x + E) = Sx + E (x ∈ E). We study mapping properties of the correspondence S → R(S), which provides a representation R of the weak Calkin algebra L(E)/W (E) (here W (E) denotes the weakly compact operators on E). Our results display strongly varying behaviour of R. For instance, there are no non–zero compact...

Let ps be the convolution kernel of the operator e −sL (see [5, (1.10), (1.11)]). When s > 0, e−sL is the solution operator for the Heisenberg heat equation ∂su = −Lu and ps is called the heat kernel (see [6, (7.30), p. 71]. The goal of this note is to study the analytic continuation of the heat kernel ps. This is interesting from the point of view of the theory of analytic hypoellipticity (see...

Decomposable mappings from the space of symmetric k-fold tensors over E, ⊗ s,k E, to the space of k-fold tensors over F , ⊗ s,k F , are those linear operators which map nonzero decomposable elements to nonzero decomposable elements. We prove that any decomposable mapping is induced by an injective linear operator between the spaces on which the tensors are defined. Moreover, if the decomposable...

The main purpose of this paper is to obtain an explicit expression of a family of matrix valued orthogonal polynomials {Pn}n, with respect to a weight W , that are eigenfunctions of a second order differential operator D. The weight W and the differential operator D were found in [12], using some aspects of the theory of the spherical functions associated to the complex projective spaces. We al...

A one-parameter symplectic group {e}t∈R derives proper canonical transformations on a Boson Fock space. It has been known that the unitary operator Ut implementing such a proper canonical transformation gives a projective unitary representation of {e}t∈R and that Ut can be expressed as a normal-ordered form. We rigorously derive the self-adjoint operator ∆(Â) and a phase factor e i ∫ t 0 τ Â (s...

It is considered whether L= lim supn→∞ n‖Tn+1 − Tn‖<∞ implies that the operator T is power-bounded. It is shown that this is so if L < 1/e, but it does not necessarily hold if L=1/e. As part of the methods, a result of Esterle is improved, showing that if σ(T )= {1} and T = I, then lim infn→∞ n‖Tn+1 − Tn‖ 1/e. The constant 1/e is sharp. Finally, a way to create many generalizations of Esterle’s...

This paper deals with a semi-classical limit(Theorem 1) by using traditional mathematical methods, and shows a Hopf theorem as a corollary. A formal discussing of it may be found in [7] 1 A semi-classical limit theorem Let M be a compact, closed Riemannian manifold of dim n, and V a vector field without degenerate zeros on M . Let Λ∗(M) be the space of differential forms on M , and D = d+ δ : Λ...

Abstract. Let A be a square matrix or a linear operator on a Hilbert space H. A dilation of A is a linear operator M on a larger space K ⊃ H such that A = PHM |H, where PH is orthogonal projection onto H. Often it is required additionally that M be a dilation of A for all or a range of positive integer powers k. While much work has been aimed at proving existence of dilations with various prope...